Liam Williams says he was "delighted" to be nominated best newcomer at the Edinburgh comedy awards last year. But no one who saw his show – a lyrical, philosophical monologue full of existential despair – could easily imagine what a delighted Williams might look like.

At the time, I wrote that this Yorkshireman, along with fellow early-twentysomething standups Bo Burnham and Alfie Brown, represented the stirrings of angry young Generation Y comedy. This is the age group who've been bequeathed austerity, corporate kleptocracy and the commodification of everything – including dissent. Small wonder they're giving us the comedy of embittered impotence. Williams's debut show was dazzlingly clever: numb to romance, jaded about selfhood and weary of the inane exertions of pop culture.

"I was excited," says the 26-year-old, "by thinking: how vulnerable can you go? How negative and how soft-souled?" He'd seen vulnerable standups before, but they stopped short, didn't make it real enough. What's distinctive about ex-Footlights man Williams is that he did much more than just send up the misery and self-indulgence. "For the six months when I was writing the show," he explains, "everything felt empty and bleak. I didn't think, 'I'll contrive an anomie-stricken persona.' I was genuinely self-pitying and depressed." By playing it for real, he was obliged to find less cliched and more novel ways to make it all funny.

The result was the most remarkable debut of last year's fringe, and Williams – hitherto best known as one-third of the sketch troupe Sheeps, with whom he still works – found himself hailed as "the Philip Larkin of British comedy". Having adapted the show into several successful "blaps", or short films, for Channel 4, he was recently commissioned to develop a series. So how does he feel about the "voice of a generation" tag? It's hard to agree, he says, "without sounding hideously grandiose".

Now Williams is back, but this time on the free fringe – partly because "you get ripped off if you do standup at the big venues"; partly (I suspect) to manage expectations; and partly because the show is called Capitalism, so it's significant to give it away for free. Even more so than last year, Williams is grappling with what it means to be young and British in 2014: "That cognitive dissonance, that contradiction in the knowledge that you are extremely privileged and yet you still think 'things are shit'. How do you balance the existential ledger?"

Specifically, he says, the show "is about wanting to write a state-of-the-nation, generation-defining piece of art and quickly accepting that I'm not capable of it, partly because I don't have any incisive notion of what capitalism is. If I wanted to do the research and read Thomas Piketty's Capital in the 21st Century then I should do that. But I sort of know I don't have the discipline. So the starting point is that visceral, instinctive anger and distrust of capitalism coming up against more rational self-analysis. 'What do you actually know? What would you actually change?' Once you accept that your heartfelt ambitions are stupid and pseudy, what are you left with?"

But isn't that a cop-out? Wouldn't we rather watch a standup who's read Piketty than someone joking about his failure to do so? "In comedy," says Williams, "there's a perennial escape route from having to say anything insightful, which is that when you hit a wall in terms of your understanding, you just go, 'Look at me, I'm an idiot.'" So is Williams taking the escape route because he wants to – or because standup convention obliges him to? "That's a good question," he says. "I oscillate between feeling that I am acquiring mastery of this art form, and worrying that, just because I've found myself earning money and can't easily leap towards any other art form, I'm stuck doing standup, much as I enjoy it."

But even that enjoyment comes and goes. My chat with Williams – enjoyable, thoughtful, frank – ends with the striking admission that he considers himself "not cut out for standup", and recently suffered "nervous breakdowns" on stage while previewing his show. "It was like being possessed," he says. "It was just being on stage without solid enough material, without reliable jokes, and reacting in the most ugly way. It was almost a tantrum."

With characteristic gloom, he concludes: "I think I'd feel happier sitting at a desk all day." This would be better, he says, than suffering "the constant need to convert material into performance. I'd like, in 30 years, to be considered a successful writer more than a successful standup. Perhaps after Edinburgh, I'll get my futile midlife crisis novel out of the way really young, then concentrate on more useful things."